Fremling Field Notebook 1978 - 1979

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IsTANEEs PR'OM

Swan STASS FOR CROSS-StTIomnaO

SLOPE 1 TO 1. ROADWAYof ANYPWDH

i

0 0

0.00

2 1

2.00 36.00

0.10

1.10 2.10

.2 .3

.4

.5

.6

.7

.8

9

0.30

0.40

0.50

0.60

0.70

0.80

0.90

3.40 4.40 5.40 6.40 7.40 8.40 9.40 10.40 11.40 12.40 13.40 14.40 15.40 16.40 17.40 18.40 19.40 20.40 21.40 22.40 23.40 24.40 25.40 26.40 27.40 28.40 29.40 30.40 81.40 32.40 33.40 34.40 35.40 36.40 37.40 38.40 39.40 40.40] 41.40 42.40 43.40 44.40 45.40 46.40 47,40 48.40 49.40 50.40

3.50 4.50 5.50 6.50 7.50 8.50 9.50 10.50 11.50 12.50 13.50 14.50 15.50 16.50 17.50 18.50 19.50 20.50 21.50 22.50 23.50 24.50 25.60 26.50 27.50 28.50 29.50 30.50 31.50 32.50 33.50 34.50 35.50 36.50 37.50 38.50 39.50 40.50 41.50 42.50 43.50 44.50 45.50 46.50 47.50 48.50 49.50 50.50

0.20

1.20 2.20

1.30 2.30

3.10 3.8,20 3.30 4.10 4.20 4.30 5.20 5.30 5.10 4 4.00 6.10 6.

20 6.30 7.10 7.20 7.30 5.00 5 8.00 8.10 8.20 8.30 8 9.30 9 9.00 9.10 9.20 10 10.00 10.10 10.20 10.30 11 11.00 11.10 11.20 11.30 12 12.00 12.10 12.20 12.30 13 13.00 13.10 13.20 13.30 14 14.00 14.10 14.20 14.30 15 1.00 15.10 15.20 15.30 16.30 47 1.00 25.00 16.10 16.20 17.20 17.30 18 18.00 17.10 18.10 18.20 18.30 19 9.00 19.10 19.20 19.30 20.00 20.10 20.20 20.30 21.00 21.10 21.20 21.30 22.00 22.10 22.20 22.30 23.00 23.10 23.20 23.30 .24.00 24.10 I24.20 24.30 25.00 25.10 25.20 25.30 26.10 26.20 26.30 2600 8 27.00 27.10 27.20 27.30 28.20 28.30 .8.00 28.10 -9.00 29.10 29.20 29.30 30.20 30.30 0.00 30.10 31.10 31.20 31.30 : 2.00 32.10 32.20 32.30 .00 33.10 33.20 33.30 34 4.00 34.10 34 20 34.30 35 10 35.20 35.30 35.00 836.10 35 86.20 36.30 36 36 00 37 37.00 37.10 37.20 37.30 38 38.00 38.10 38,20 38.30 .39 39.00 39.10 30.20 39.30 40.20 40.30 40 40.00 4.00 40.10 41.10 41.20 41.30 41l 41.00 42 42.00 42.10 42.20 42.30 43.10 43.20 43.30 -43 43.00 "44 44.00 44.10 44.20 44.30 "45 45.00 45.,10 45.20 45.30 -48 48.00 46.10 46.20 46.30 47.10 47.20 47.30 47 47.00 48 48.00 48.10 48.20 48:30 49 49.00 49.10 49.20 49.30 so 50.00 50.10 50.20 50.30 I

1.40 2.40

1.50 2.50

I

1.60 2.60

1.70 2.70

3.60 1.70 4.60 4.70 5.70 5.60 6.670.70 7.60 7.70 8.60 8.70 9.60 9.70 10.60 10.70 11.60 11.70 12.60 12.70 13.60 13.70 14.60 14.70 15.60 15.70 16.60 16.70 17.60 17.70 18.60 18.70 19.60 19.70 20.60 20.70 21.60 21.70 22.60 22.70 23.60 23.70 24.60 24.70 25.60 25.70 26.60 26.70 27.60 27.70 28.60 28.70 29.60 29.70 30.60 30.70 31.60 31.70 32.60 32.70 33.60 33.70 34.60 34.70 35.60 35.70 36,60 36.70 37.60 7.70 38.60 .38.70 39.60 39.70 40.60 40.70 41.60 41.70 42.60 42.70 43.60 43.70 44.60 44.70 45.60 45.70 46.60 46.70 47.60 47.70 48.60 48.70 49.60 49.70 50.60 50.70

1.80 2.80

1.90 2.90

3.80 3.90 4.80 4.90 5.80 5.90 .80 .90 7.80 7.90 8.90 8.80 9.80 9.90 10.80 10.90 11.80 11.90 12.80 12.90 13.80 13.90 14.80 14.90 15.80' 15.90 16.80 16.90 17.80 17.90 18.80 18.90 19.80 19.90 20.80 20.90 21.80 21.90 22.80 22.90 23.80 23.90 24.80 24.90 25.80 25.90 26.80 26.90 27.80 27.90 28.80 28.90 29.80l 29.90 30.80 30.90 31.80 31.90 32.80 32.90 33.80 33.90 34.80 34.90 35.80 35.90 36.80 36.90 37.80 37.90 38.80 [38.90 39.80 39.90 40.80 40.90 41.80 41.90 42.80 42.90 43.80 43.90 44.80 44.90 45.80 45.90 46.80 46.90 47.80 47.90 48.80 48.90 49.80 49.90 50.80 50.90 |

0

1 2 3 4

5 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 28 24 25 26 27 2 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 4 47 48 49 50 fil

Distance of slope stake from side or shoulder stake for any width roadway, slope 1 to 1. It ground is nearly level the cut or 811 at side stake is located by the double entry method in left Column and to p row. 1 he number in body of table in same row and column gives distance from side stake to slope stake. It ground is not level estimate the difference in elevation between the side stake and slope stake, lower target by this amount if cut, elevate if fill. Add this amount to and fnd distance in table. Set up rod at this point, and line of sight should cut target. cut or If It does not make the slight adjustment necessary.

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IMPROVED

TABLES

AND

INFORMATION

DIRECTIONS FOR USE OF TABLES TABLE No. XIV Distance of slope stake from side or shoulder to 1. stake for any width roadway, slope 1 If ground is nearly level, the cut or fill at side stake is located by the double entry method in left column and top row. The number in body of table in same row and column gives distance from side stake to slope stake. If ground is not level estimate the difference in elevation between the side stake and slope stake, lower target by this amount if cut, elevate if 11fill.Add this amount to cut or fill and find distance in table.

Set up rod at this point, and line of sight should cut target. If it does not make the slight adjustment necessary.

TABLE No. VIII To find Tangent and External for curve of any other degree, divide by degree of curve and add correction found in column of corrections.

Degree of curve with a given I may be foidnd by dividing tangent, (or external), opposite I by given tangent, (or external).

The distance from a point on the tangent to the curve is very nearly the square of the tangent length divided by twice the radius.

TABLE II TRIGONOMETRIC FORMUL E. LA = LMOP LB =LPON= LOPL R= OB = c= 1 sin A

b

1

a b

OM

NT

NT

OM OT

1 OT

cot A

vers A covers A

1

-

c

tan A=

csc A=

a

c

b

sos A-=-

see A=

a

=

.

ON LM

= a -= sos B = LP -sin b

-

I

B= OL

MQ MQ 1 = NT =

cotB=MQ tan B = NT

= OQ = csc B = OQ = OT = sec B = OT

= LM =

OP OP-LP

covers B +#

= OP-LP = vers B OP exsec A= PQ = coexsec B coexsec A PT = exsec B 1- C in osA /+Cos A sin

s/s A=

-

2

cos

1/* A=

2

2 sin A cos A cos 2 A = cos t A-sint A sin A sin B sin C' Law of Lines a B C Law of Cosines c'=!-a+b'-2 ab cos C sin 2 A

Law of Tangents a+b a-b

== tan 'i, (A+B)

tan '/2 (A-B)

TABLE II -- Continued

TRIGONOMETRIC FORMULJE (continued) in any triangle: Given a, b, C; to find c, B, A. Use Law of Lines.

Given A, B, c; to find a, b, C. Use Law of Lines.

Given a, b, c; to find A, B, C. Let a+b--c

(s-a) (s-b) (s-c)

,

r

8

2

s (s--a)

cos '/ A =-

tan I'/ A

r s-a

tan 't B =

s--b

r s-c Area of a triangle: Area= s'Iab Sin C Area= Is (s--a) (s-b) (s-c) tan '/s C

PRISMOIDAL :FORMULA.

-1-b+-4M)

Vol. =

h = altitude; b, B = bases; M = midsection TABLE II

INCHES AND FRACTIONS OF AN INCH IN DECIMALS OF A FOOT 0 'es .0052

.0104

as.0156

./4.0208 */s .0260 $i .0313 ,is .0365 'is .0417 he 1.0469 /Is .0521 /is.0573 S,4 .0625 ,/is .0677 • .0729 u/ss .0781 1 .0833 0

1

2

3

4

5

6

7

8

9

10

11

.0885 .0938 .0990 .1042 .1094 .1146 .1198 .1250 .1302 .1354 .1406 .1458 ,1510 .1563 .1615 .1667

.1719 .1771 .1823 .1875 .1927 .1979 .2031 .2083 .2135 .2188 .2240 .2292 .2344 .2396 .2448 .2500

.2552 .2604 .2656 .2708 .2760 .2813 .2865 .2917 .2969 .3021 .3073 .3125 .3177 .3229 .3281 .3333

.3385 .3438 .3490 .3542 .3594 .3646 .3698 .3750 .3803 .3854 .3906 .3958 .4010 .4063 .4115 .4167

.4219 .4271 .4323 .4375 .4427 .4479 .4531 .4583 .4635 .4688 .4740 .4792 .4844 .4896 .4948 .5000

.5052 .5104 .5156 .5208 .5260 .5313 .5365 .5417 .5469 .5521 .5573 .5625 .5677 .5729 .5781 .5833

.5885 .5938 .5990 .6042 .6094 .6146 .6198 .6250 .6302 .6354 .6406 .6458 .6510 .6563 .6615 .6667

.6719 .6771 .6823 .6875 .6927 .6979 .7031 .7063 .7135 .7188 *7240 .7292 .7344 .7396 .7448 .7500

.7552 .7604 .7656 .7708 .7760 .7813 .7865 .7917 .7969 .8021 .8073 .8125 .8177 .8229 .8281 .8333

.8385 .8438 .8490 .8542 .8594 .8646 .8698 .8750 .8802 .8854 .8906 .8958 .9010 .9063 .9115 .9167;

.9219 .9271 .9323 .9375 .9427 .9479 .9531 .9583 .9635 .9688 .9740 .9792 .9844 .9896 .9948 1.000

1

2

3j4

71

8

5

6

9

10

11

sJ/s

' [/i

s/.

tl

I/t [/s

s/is

S/s I", 1 s

I'.z/

l's

uj.

1

TABLE IV

Deg.

Radius

Mid. Ord.

-RADII,

Tan. Offset

.145 .291. .436 .582 .727

ORDINATES Def. for 1 Foot

0o 10' 34377.5 20 17188.8 30 11459.2 40 8594.42 50 6875.55

.036 .073 .109 .145 .182

1 10 20 30 40 50

5729.65 4911.15 4297.28 3819.83 3437.87 3125.36

.218 .255 .291 .327 .364 .400

.873 1.018 1.164 1.309 1.454 1.600

0.30 0.35 0.40 0.45 0.50 0.55

10 20 30 40 50

2864.93 2644.58 2455.70 2292.01 2148.79 2022.41

.436 .473 .509 .545 .582 .618

1.745 1.891 2.036 2.181 2.327 2.472

0.60 0.65 0.70 0.75 0.80 0.85

10 20 30 40 50

1910.08 1P09.57 1719.12 1637.28 1562 88 1494.95

.655 .691 .727 764 .800 836

2.618 2.763 2.908 3.054 3.199 3.345

0.90 0.95 1.00 1.05 1.10' 1.15

1432.69 .873 10 1375.40 .909 20 1322.53 .945 30 1273.567.982 40 1228.11 1.018 50 1185.78 1.055

3.490 3.635 3.718 3.926 4.071 4.217

1.20 1.25 1.30 1.35 1.40 1.45

1146.28 1109.33 1074.68 1042.14 1011.51 982.64

1.091 1.127 1.164 1.200 1.237 1.273

4.362 4.507 4.653 4.798 4.943 5.088

1.50 1.55 1.60 1.65 1.70 1.75

955.37 8929.57 905.13 881.95 859.92

1.309 1.346 1.382 1.418 1.455

5.234 5.379 5.524 5.669 5.814

1.80 1.85 1.90 1.95 2.00

2

S

4

6

Note.

AND DEFLECrTONs

Deg.

0.05'

0.10 0.15 0.20 0.25

Cbord Deflection =-2 times tangent deflection.

Tan. Offset

Def. for Foot

1.528 1.600 1.637 1.673

6.105 6.395 6.540 6.685

2.10' 2.20 2.25 2.30

716.78 1.746 688.16 1.819 674.69 1.855 6681.74 1.892

6.976 7.266 7.411 7.556

2.40 2.50 2.55 2.60

637.28 614.56 603.80 593.42

1.965 2.037 2.074 2.110

7.846 8.136 8.281 8.426

2.70 2.80 2.85 2.90

573.69 546.44 521.67 499.06 478.34 459.28 441.68 425.40 410.28 396.20

2.183 2.292 2.402 2.511, 2.620.

2.730 2.839 2.949 3.058 3.168

8.716 9.150 9.585 10.02 10.45 10.89 11.32 11.75 12.18 12.62

3.00 3.15 3.30 3.45 3.60 3.75 3.90 4.05 4.20 4.35

383.07 370.78 359.27 348.45 338.27 319.62 302.94

3.277 3.387 3.496 3.606 3.716 3.9356 4.155

13.05 13.49 13.92 14.35 14.78 15.64 16.51

4.50 4.65 4.89 4.95 5.10 5.40 5.70

287.94 274.37 262.04 250.79 240.49

4.374 4.594 4.814 5.035 5.255

17.37 18.22 19.08 19.94 20.79

6.00 6.30 6.60 6.90 7.20

231.01 222.27 214.18 206.68 199.70 193.18

5.476 5.697 5.918 6.139 6.360 6.583

21.64 22.50 23.35 24.19 25.04 25.88

7.50 7.80 8.10 8.40 8.70 9.00

Radius

Mid. Ord. I

819.02 781.84 764.49 747.89

(1)c =

V TABLE V CURVE FORMULJE FOR SIMPLE CURVES COMPILED BY J.CALVIN LOCKE, C. E. 9 a/2R (2) c-= 1 1a'-+b*

(3) c- 1/2R (R- V(R+b) (R-b)= V2R (R(4) c =2 m (2R-m) 1 I (6)c = 2T cos /I 1 (5) c - 2R sin /2 1 /,I (7) e= R exsee 1

e = R tan /l Itan '/4 i (10) b - 'a (2R-a)

(11)

2+ j

b/(c b= Rsin I R=

a + b

=

2a

(9) e = T tan '/.

c vc-41 c- *) 1 (13) b= a cot /sI (15) R =

C-

2,(18)

(20) m = RT

cf4mg

d2 2m

2a

d = fR (2R-/(2R+c) 2R-c) = (17) d =

-- b')

Sm

R (2R-

d = 2R sin '/4 I R-

(R+

2

4R'-cO -(19) m =2

= R+

VR-

4

(21) m = R vers '/1 (22) m = R sin 1/l1 tan '/4 I (23) m = '/s ctan t'4 I (25) a= R - (R+b)(R--b)= R- /R'-b' 2 (24). a (28 a = R sin Itan 1l (27) a = R vers I 1)1 a 2 R (sin g '/2 ( (31) T - Rtan 1 /sI I (30) a =TsinI 29 a =b tan

=/s

(32) I -

X 57.295780

(34) L = IR X 0.01745329 (36 Area Seg.

X 57.295780

(33) R =

3 (35) L = 8d-c 3

LR-R' sin I

LR-Rb

2

2

TABLE VI

SINES, COSINES, TANGENTS, COTANGENTS tan 0'

sin 10'

tan sin 10' 20'

tan sin 20' 30'

tan sin 30' 40'

tan sin 40' 50'

0000 175 349' 523 698 872 1045 219 392 564

0000 0175 349 524 699 875 1051 228 405 584

0029 0204 378 552 . 727 901 1074 248 421 593

0029 0058 0204 0233 378 407 553 581 729 756 904 929 1080 1103 257 279 435 449 614 622

0058 0087 0233 0262 407 436 582 610 758 785 934 958 1110 1132 287 305 465 478 644 650

0087 0116 262 291 "437 465 612 640 787 814 963 987 1139 1161 317 334 495 507 673 679

0116 0145 291 320 466 494 641 669 816 843 992 1016 1169 190 346 363 524 536 703 708

0145 320 495 670 846 1022 198 376 554 733

89 88 87 86 85 84 83 82 81 80

10 736 11 908 12 .2079 13 250 14 419 15 588 16 756 17 924 18 3090 19 256

763 765 944 937 2126 2108 309 278 493 447 679 616 867 784 3057 952 249 3118 443 283

793 794 974 965 2156 2136 339 306 524 476 711 644 899 812 3089 939 281 3145 476 311

823 822 2004 994 186 2164 370 334 555 504 742 672 931 840 3121 3007 314 173 508 338

853 851 2035 2022 217 193 401 363 586 532 773 700 962 868 3153 3035 346 201 541 365

883 880 2065 2051 247 221 432 391 617 560 805 728 994 896 3185 3062 378 228 574 393

914 2Q95 278 462 648 836 3026 217 411 607

79 78 77 76 75 74 73 72 71 70

20 21 22 23 24 25 26 27, 28 29

640 448 839 611 4040 773 245 934 452 4094 663 253 877 410 5095 566 317 720 543 874

673 475 872 638 4074 800 279 961 487 4120 699 279 913 436 5132 592 354 746 581 899

706 502 906 665 4108 827 314 987 522 4147 734 305 950 4462 5169 617 392 772 619 924

739 529 939 692 4142 854 348 4014 557 173 770 331 986 488 5206 643 430 797 658 950

772 973 4176 383 592 806 '5022 243 467 696

557 719 881 4041 200 358 514 669 823 975

805 4006 210 417 628 841 5059 280 505 735

69 68 67 66 65 64 63 62 61 60

774 6009 249 494 745 7002 265 "536 813 8098

5812 5050 6048 200 289 348 536 495 787 640 7046 783 310 925 581 6065 860 202 8146 338

851 5075 6088 225 330 5373 577 519 830 664 7089 807 355 948 627 6088 907 225 8195 361

890 5100 6128 250 371 398 619 544 873 688 7133 831 400 972 673 6111 954 248 8243 383

930 5125 6168 275 412 422 661 568 916 712 7177 854 445 995 720 6134 8002 271 292 406

969 6208 453 703 959 7221 490 766 8050 342

59 58 37 56 55 54 53 52 51 50

40 428 391 450 441 472 491 494 541 517 594 539 642 899 670 952 744 604 796 626 847 648 41 561 693 583 42 691 9004 713 9057 734 9110 756 9163 777 9217 799 9271 43 820 325 841 380 862 435 884 490 905 545 926 601 44 947 657 967 713 988 770 7009 827 7030 884 7050 942 45 7071 1.0000 7692 1.0058 7112 1.0117 133 1.0176 153 1.0235 173 1.0295

49 48 47 46 45 44

0 I 2 3 4 5 6 7 8 9

420 584 746 907 4067 226 384 540 695 848

30 5000 31 150 32 299 33 446 341592 35 736 36 878 37 6018 38 157 39 293

S160 ' .

cos

5025 175 324 471 016 760 901 6041 180 316

60' 50' cot

cos

50' 40' cot

cos

tan 50'

& V

sin 0'

t -

40' 30'

30' 20'

20' 10'

10'

cot

cot

cot

cot

cos

cos

cos

s

.8

TABLE VI (continued) SINES, COSINES, TANGENTS, COTANGENTS (continued)

o sin a

0'

tan sin

tan sin

0'

10'

10'

20'

tan sin tan sin 20'

30'

30'

40'

tan

sin

tan

40'

50'

50'

o v

46 7193 1.0355 7214 1.0416 7234 1.0477 7254 1,0533 7274 1.0599 7294 1.0661 43 47 314 .0724 333 .0786 353 .0850 373 .0013 392 .0977 412 .1041 42 48 431 .1106 451 .1171 470 .1237 490 .1303 509 .1369 528 .1436 41 49 547 .1504 566 ..1571 585 .1640 604 .1708 623 .1778 642 .1847140 50 660 1.1918 7679 1.1988 7698 1.2059 7716 1.2131 7735 1.2203 7753 1.2h6 862 .2723 51 771 .2349 790 .2423 808 .2497 826 .2572 844 .2647 52 880 .2799 898 .2876 916 .2954 934 .3032 951 .3111 969 .3190 53 986 .3270 8004 .3351 8021 .3452 8039 .3514 8056 .3597 8073 .3680 54 8090 .3764 107 .3848 124 .3934 141 .4019 158 .4106 175 .4193 55 192 ' .4281 208 .4370 225 .4460 241 .4550 258 .4641 274 .4733 56 290 .4826 307 .4919 323 .5013 339 .5108 355 .5204 371 .5301 57 387 .5399 403 .5497 418 .5597 434 .5697 450 .5798 465 .5900 58 480 ,6003 496 .6107 511 .6212 526 .6319 542 .6426 557 .6534 59 572 .6643 587 .6753 601 .6864 616 .6977 631 .7090 646 .7205

39 38 37 36 35 34 33 32 31 30

60

29 28 27 26 25 24 23 22 21 20

660 1.7321 8675 1.7437 8689 1.7556 8704 1.7675 8718 1.7797 61 746 .8040 760 .8165 774 .8291 788 .8418 802 .8546 62 829 .8807 843 .8940 857 .9074 870 .9210 884 .9347 63 910 .9626 923 .9768 936 .9912 949 2.0057 962 2.0204 64 988 2.0503 9001 2.0655 9013 2.0809 9026 .0965 9038 .1123 65 9063 .1445 075 .1609 088 .1775 100 .1943 112 .2113 66 135 .2460 147 .2637 159 .2817 171 .2998 182 .3183 67 205 .3559 216 .3750 228 .3945 239 .4142 250 .4342 68 272 .4751 283 .4960 293 .5172 304 .5386 315 .5605 69 336 .6051 346 .6279 356 .6511 367 .6746 377 .6985

70 71 72 73 74 75 76 77 78 79

8732 1.7917 816 .8676 897 .9486 975 2.0353 9051 .1283 124 .2286 194 .3369 261 .4545 325 .5826 38171 .7228

3971 2.7475 9407 2.7725 9417 2.7980 9426 2.8239 9436 2.8502 9446 2.8770 19 455 .9042 465 .9319 474 .9600 483 .9887 492 3.0178 502 3.0475 18 511 3.0777 520 3.1084 528 3.1397. 537 3.1716 546 .2041 555 .2371 17 563 .2709 572 .3052 580 .3402 588 .3759 596 .4124 605 .4495 16 613 .4874 621 .5261 628 .5656 636 .6059 644 .6470 652 .6891 15 659 .7321 667 .7760 674 .8208 681 .8657 689 .9136 696 .9617 14 703 4.0108 710 4.0611 717 4.1126 724 4.1653 730 4.2193 737 4.2747 13 744 .3315 750 .3897 757 .4494 763 .5107 769 .5736 775 .6382 12 781 .7046 787 .7729 793 .8430 799 .9152 805 .9894 811 5.0658 11 816 .1446 822 5.2257 827 5.3093 833 5.3955 838 5.4845 843 .5704 10

80 9848 5.6713 9853 5.7694 9858 5.8708 9863 81 877 6.3138 881 6.4348 886 6.5606 890 82 903 7.1154 907 7.2687 911 7.4287 914 83 925 8.1443 929 8.3450 932 8.5555 936 84 945 9.5144 948 9.7882 951 10.078 954 85 962 11.430 964 11.826 967 12.250 969 86 976 14.300 978 14.924 980 15.605 981 87 986 19.081 988 20.206 989 21.470 990 88 994 28.636 9995 31.242 9996 34.308 997 89 9998 57.290 9999 68.750 9999 85.940 9999

60 cos

60' 50' cot cos

50' 40' cot cos

40' 30' cot cos

5.9758 9868 6.0844 9872 6.6912 894 .8209 899 7.5958 918 7.7704 932 8.7769 939 9.0098 942 10.385 957 10.711 959 12.706 971 13.197 974 16.350 983 17.169 985 22.903 992 24.542 993 38.189 997 42.964 9998 114.58 1.000 171.88 1.000

30' cot

20' cos

20' cot

10' cos

6.1970 .9682 7.9530 9.2553 11.059 13.727 18.075 26.432 49.104 343.77

10' o cot

9 8 7 6 5 4 3 2 1 0

.

TABLE VII Deflections for Sub Chords for Short Radius Curves.

Radius sub chord sn of def. angle ength of 50 sin of d an of arc

Degree Curve

sin.

I def. ang.

12.5 Ft.

15 Ft.

20 Ft.

25 Ft.

for 100 ft.

30o 320 340

193.18

1 51'

20 17'

20 58'

3 43'

181.39 171.01

1059' ° 2 06'

2 25' ° 2 33

3 10o' 3 21'

38' 4 12'

360 380 40 42

161.8o 153.58

2 2 2 2

2 41' 249 ' 2 57' 3 05 3 13' 3 21'

3 3' 344 3 55 4 07

4 26' 4 40' 4 54 5 08'

10o.15 101.33 101.48 Ior.66

3 291 ' 3 38 30 46'

5050 6 04' 60 17'

6044

104.14

6057 ° t 70 1'

10.7 104.72

°

146.19

139.52

13 20' 27 34'

44 °

133.47

46

127.97

48°

122.92

50

118.31

52 ° 54 560

I114.06

3

16'

30 54'

1o6.50

3

22'

4002'

4 40 4 51 5002' 50 5 23

580°

103. 14

3

29 , 35' 30

410o'

534

40 18'

544'

60

20 4 2 48' 0 55' 3 02 30 o09'

10.1 100.00

T = Rtan I 50 tan I Sin. J D

Sin. J D =

40'18

4 29'

R = T cot. j I

Sin. D R = 50

Lo R

E = R ex. sec j I E = T tan & I

I--

°

5022

'

5 36'

6031

zoi.85 o02.o6 102.29 102.53

102.76 103.00 103.24 103.54

103.84 104.43

Chord def. =chord R

No. chords=

Sin. j D = 50 tan I Tan. def.= chord def.

T The square of any distance, divided by twice the radius, will equal the distance from tangent to curve, very nearly.

To find angle for a given distance and deflection.

Rule I. Multiply the given distance by .01745 (def. for 1o for I ft. see Table II.), and divide given deflection by the product.

Rule 2. Multiply given deflection by 57.3, and divide the product by the given distance.

To find deflection for a given angle and distance. Multiply the angle by .o0745, and the product by the distance.

GENERAL DATA RIGHT ANGLE TRIANGLES. Square the altitude, divide by twice the base. Add quotient to base for hypotenuse.

Given Base Ioo, Alt. Io.o1+02S200=.5. I0oo.5=oo0.5 hyp.

Given Hyp. 1oo, Alt. 25.25+200oo=3.25. 100-3.125 =96.875=Base.

Error in first example, .oo2; in last, .045.

To find Tons of Rail in one mile of track: multiply weight per yard

by I1,and divide by 7.

LEVELING. The correction for curvature and refraction, in feetand decimals of feet is equal to 0.574ds, where d is the distance in miles.

The correction for curvature alone is closely, jd*. The combined correction is negative.

PROBABLE ERROR. If dj, d., d,, etc. are the discrepancies of various results from the mean, and if Id'=the sum of the squares of these differences and n=the number of observations, then the probable error of the

mean=-

0.6745

I n (n-1)

TANGENTS AND EXTERNALS TO A 10 CURVE.

TABLE VIII I

T

50.00 58.34 20' 66.67 75.01 30' 40'. 83.34 50' 91.68 100.01 20 10' 108.35 20' 116.68 30' .125.02 40" 133.36 50- 141.70 30o 150.04 10' 158.38 20' 166.72 30' 175.06 40' 183.40 50' 191.74 200.08 40 10" 208.43 20' 216.77 30' 225.12 40" 233.47 50' 241.81 50 250.16 10' 258.51 20' 266.86 30' 275.21 40' 283.57 50' 291.92 300.28 6o 10' 308.64 20' 316.99 30' 325.35 40' 333.71 p0'. 342.08 350.44 70 358.81 367.17 30' 375.54 40' 383.91 50' 392.28 400.66 10' 409.03 20' 417.41 30' 425.79 40' "434.17 50' 442.55 o90 450.93 10' 459.32 467.71 30' 476.10 40' 484.49 50' 492.88 10o 501.28 10' 509.68 30' 518.08 526.48 40' 534.89 50' 543.29 t0

10'

1=1o

E

I

o

11 .218 10' .297 20' .388 + 30' .491 50C. T 40' .606 50' .733 .03 E .873 .001 120 1.024

1.188 30' 1.364 40' 1.552 1.752 50' 1.964 100 C. 10 2.188 10' 20' 2.425 .06 30' 2.674 E 40' 2.934 .003 3.207 50' 3.492 10' 3.790 20' 4.099 30' 4.421 40' 4.755 5.100 150 C. 50' T 5.459 .09 150 5.829 10' E 6.211 .004 20' 6.606 30' 7.013 40' 50' 7.432 7.863 160 8.307 10' 8.762 20' 9.230 30' 40' 9.710 10.202 .13 50' E 10.707 10 .006 11.224 10' 11.753 20' 12.294 30' 12.847 40 13.413 50' 13.991 180 0 14.582 25 C. 10' 15.184 T 20' 15.799 .16 30' E 16.426 40' 50' 17.065 .007 17.717 190 18.381 10' 19.058 20' 19.746 30' 40' 20.447 21.161 300 C. 50' T 21.887 200 22.624 .19 10' E 23.375 20' 24.138 30' 24.913 40' 25.700 50' T=

I R tan'1i1

E

T

551.70 560.11 568.53 576.95 585.36 593.79 602.21 610.64 619.07 627.50 635.93 644.37 652.81 661.25 669.70 678.15 686.60 695.06 703.51 711.97 720.44 728.90 737.37 745.85 754.32 762.80 771.29 779.77 788.26 796.75 805.25 813.75 822.25 830.76 839.27 847.78 856.30 864.82 873.35 881.88 890.41 898.95 907.49 916.03 924.58 933.13 941.69 950.25 958.81 967.38 975.96 984.53 993. 12 1001.7 1010.3 1018.9 1027.5 1036,1 1044.7 1053.3

I

210 26.500 10' 27.313 20' 28.137 30' 28.974 T 40' 29.824 50' 30.686 .06 E 31.561 :.006 220 10' 32.447 20' 33.347 30' 34.259 40' 35.183 50' 36.120 37.070 100 CG 230 10' 38.031 39.006 .13 20' 30' 39.993 E 40.992 40' 42.004 50' 43.029 24o 44.066 10' 45.116 20' 46.1781 30' 40' 47.253 48.341 150 C. 50' T 49.441 .19 250 50.554 10' E 51.679 .017 20' 52.818 30' 53.969' 40' 55.132 50' 56.309 2 o 10' 57.498 58.699 20' 59.914 200 C. 30' 61.141 40' 62.381 .26 50' E 63.634 270 64.900 .022 10' 66.178 20' 67.470 30' 68.774.

40' 70.091 50' 280 71.421 72.764 250 C, 10' 74.119 T 20' 75.488 .32 30' 76.869 E 78.264 .028 50' 79'.671 2930 40' 81.092 10' 82.525 20' 30" 83.972 30' 85.431 40' 86.904 30 0 C. 50' 88.389 T 300 89.888 .39 10' E 91.399 20' 92.924 .034 30' 94.462 40' 96.013 50'

II

E = R exsec

E

T

I

I=20

I

its

I=.300

1061.9 97.577 1070.6 99.155 1079.2 100.75 1087.8 102.35 50 C. T 1096.4 103.97 1105.1 105.60 .10 E 1113.7 107.24 .013 1122.4 108.90 1131.0110.57 1139.7 112.25 1148.4 113.95 1157.0 115.66 1165.7 117.38 100 C. 1174.4 119.12 T 1183.1 120.87 .19 1191.8 122.63 E 1200.5 124.41 .025 1209.'2 126.20 1217.9 128.00 1226.6 129.82 1235.3 131.65 1244.0 133.50 1252.8 135.35 1261.5137.23 150 C. T 1270.2 139.11 .29 1279.0 141.01 E 1287.7 142.93 .038 1296.5 144.85 1305.3 146.79 1314.0 148.75 1322.8 150.71 1331.6 *152.69 1340.4 154.69 1349.2 156.70 200 C. 1358.0 158.72 T 1366.8 160.76 .39 E 1375.6 162.81 1384.4 164.86 .051 1393.2 166.95 1402.0 169.04 1410.9 171.15 1419.7 173.27 1428.6 175.41 1437.4 177.55 250 C. 1446.3 179.72 T 1455.1 181.89 .49 184.08 E 1464.0 1472.9 186.29 .065 1481.8188.51 1490.7, 190.74 1499.6 192.99 1508.5 195.25 1517.4 197.53 1526.3 199.82 300 C. T 1535.3 202.12 1544.2 204.44 .59 E 1553.1 206.77 1562.1 209.12 .078 1571.0 211.48 1580.0 213.86,

I~

1

TABLE VIII TANGENTS AND EXTERNALS TO A IT

E

I

I=40@

T

E

1589.0 1598.0 1606.9 1615.9 1624.9 1633.9 1643.0 1652.0 1661.0 1670.0 1679.1 1688.1 1697.2 $$o 10' 1706.3 20' 1715.3 30' 1724.4 40' 1733.5 50' 1742.6 340 .1751.7 10' 1760.8 20' 1770.0 30' 1779.1 40' 1788.2 50' 1797.4 1806.6 $ 1a 10' 1815.7 20' 1824.9 30' 1834.1 40' 1843.3 50' 1852.5 1861.7 360 10' 1870.9 20' 1880.1 1889.4 30' 1898.6 1907.9 1917.1 10' 1926.4 20' 1935.7 30' 1945.0 40' 1954.3 50' 1963.6 1972.9 380 10' 1982.2 20' 1991.5 30' 2000.9 40' 2010.2 50' 2019.6 30 2029.0 10' 2038.4 2047.8 30' 2057.2 40' 2066.6 50' 2076.0 2085.4 400 10' 2094.9 20' 2104.3 30' 2113.8 40' 2123.3 50' 2132.7 310 10' 20' 30' 40' 50' 820 10' 20' 30' 40' 50'

248.7 251.3 253.9 256.5 259.1 261.8 264.5 267.2 269.9 272.6 275.3 278.1 280.8 283.6 286.4 289.2 292.0 294.9 297.7 300.6 303.5 306.4 305.3 312.2 315.2 318.1 321.1 324.1 327.1" 330.2 333.2 336.3 339.3 342.4 345.5 348.6 351.8 354.9 358.1 361.3 364.5 367.7 371.0 374.2 377.5 380.8 384.1

100 C.

43o

10' 20' .26 30' E 40' .046 50' 44o 10' 20' 30' 40' 150 C. 50' .40

450

10' 20' 30' 40' 50' 460 10' 20' 20o C. 30' 40' T 50' .53

E

.070

E .093

250

C,

.67 .117

T

E

2732.9 2743.1 2753.4 2763.7 2773.9 2784.2 2794.5 2804.9 2815.2 2825.6 2835.9 2846.3 2856.7 2867.1 2877.5 2888.0 2898.4 2908.9 2919.4 2929.9 2940.4 2951.0 2961.5 2972.1 2982.7 2993.3 3003.9 3014.5 3025.2 3035.8 3046.5 3057.2 3067.9 3078.7 3089.4 3100.2 3110.9 3121.7 3132.6 3143.4 3154.2 3165.1 3176.0 3186.9 3197.8 3208.8 3219.7 3230.7 3241.7 3252.7 3263.7 3274.8 3285.8 3296.9 3308.0 3319.1 3330.3 3341.4 3352.6 3363.81

618.4 622.8 627.2 631.7 636.2 640.7 645.2 649.7 654.3 658.8 663.4 668.0 672.7 677.3 682.0 686.7 691.4 696.3 700.9 705.7 710.5 715.3 720.1

I=tOo

"

216.3 410 + 10' 218.7 20' 221.1 5 C. T 223.5 30' 226.0 .13 40' E 50' 228.4 .023 230.9 420 10' 233.4 20' 235.9 238.4 30' 40' 241.0 243.5 50' 246.1

I

I=5o1E

"

1e CURVE:

470

10' 20' 30' 40' 50' 480 10' 20' 30' 40' 50' 490

10' 20' 30' 40' 50' 300 C. 500 10' .80 20' E s30' .141 40' 50'

T= R tan $is t

2142.2 2151.7 2161.2 2170.8 2180.3 2189.9 2199.4 2209.0 2218.6 2228.1 2237.7 2247.3 2257.0 2266.6 2276.2 2285.9 2295.6 2305.2 2314.9 2324.6 2334.3 2344.1 2353.8 2363.5 2373.3 2383.1 2392.8 2402.6 2412.4 2422.3 2432.1 2441.9 2451.8 2461.7 2471.5 2481.4 2491.3 2501.2 2511.2 25121.1 2531.1 2541.0 2551.0 2561.0 2571.0 2581.0 2591.0 2601.1 2611.2 2621.2 2631.3 2641.4 2651.5 2661.6 2671.8 2681.9 2692.1 2702.3 2712.5 2722.7

387.4 390.7 394.1 397.4 400.8 404.2 407.6 411.1 414,5 418.0 421.4 425.0 428.5 432.0 435.6 439.2 442.8 446.4 450.0 453.6 457.3 461.0 464.6 468.4 472.1 475.8 479.6 483.4 487.2 491.0 494.8 498.7 502.5 506.4 510.3 514.3 518.2 522.2 526.1 530.1 534.2 538.2 542.2 546.3 550.4 554.5 558.6 562.8 566.9 571.1 575.3 579.5 583.8 588.0 592.3 596.6 600.9 605.3 609.6 614.0

510to

10' 20' SoC. 30' T 40' .17 50' E .037 520 10' 20' 30' 40' 50' 100 C. T .34 E .075

50o

10' 20' 30' 40' 50' 540

150 C.

10' 20 30' 40' 50' 550

E .116

10' 20' 30' 40'

50' 5o0 10' 20' 200 C. 30" 40' 50" .68

E

.151

570

10' 20' 30 40' 50'

580 10' 250 C. 20' T 30' .85 40' E 50' .189 590

10' 20' 30' 40' 50' 30

C.

T 1.02

E

.227

10' 20' 30 40' 50'

E= Rexsec

'itI

725.0

5 C. T .21 E

.056

100 C. T .42

E

.112

150 C.

T 729.9 734.8 E 739.7 .168 744.6 749.6 754.6 759.6 764.6 769.7 774.7 200 C. 779.8 T 784.9 .81 E 790.1 795.2 .225 800.4 805.6 810.9 816.1 821.4 826.7 25 C. 832.0 837.3 1.05 842.7 E 848.1 2.83 853.5 858.9 864.3 869.8 875.3 880.8 C. 886.4 300 T 892.0 1.27 897.5 E 903.2 .340 908.8 914.5.

--

CURVE TABLE VIII TANGENTS AND EXTERNALS TO A o10 1

T

610 10' 20'

30' 40' 50' 620 10' 20' 30' 40' 50' 630 10' 20' 30' 40' 50'

640 10' 20' 30' 40' 50' 10' 20' 30'

40' 50'

60

10' 20'

30' 40' 50' 670 10' 20' 30' 40' 50' 680 10'

20

30' 40' 50 T9 10'

20' 30' 40' 50' 700 30' 40 50'

E

I=70011

I

T

710 4086.'9 3375.0 920.2 10' 4099.5 3386.3 925.9 + 20' 4112.1 3397.5 931.6 30' 4124.8 3408.8 937.3 sTC. 40' 1137.4 3420.1 943.1 50' 4150.1 3431.4 948.9 .25 E 4162.8 3442.7 954.8 .080 720 10' 4175.6 3454.1 960.6 3465.4 966.5 20' 4188.5 30' 4201.2 3476.8 972.4 40' 4214.0 3488.3 978.3 50' 4226.8 3499.7 984.3 o 4239.7 3511.1 990.2 100 C 73 10' 4252.6 3522.6 996.2 T 20' 3534.1 1002.3 4265.6 .51 3545.6 1008.3 30' 4278.5 E 40' 4291.5 3557.2 1014.4 159 50' 4304.6 3568.7 1020.5 3580.3 1026.6 740 4317.6 3591,9 1032.8 10' 4330.7 3603.5' 1039.0 20' 4343.8 3615.1 1045.2 30' 4356.9 40' 4370.1 3626.8 1051.4 3638.5 1057.7 150 C 6' 4383.3 750 4396.5 3650.2 1063.9 3661.9 1070.2 o10' 4409.8 E. 20' 4423.1 3673.7 1076.6 .240 3685.4 1082.9 30' 4436.4 3697.2 1089.3 40' 4449.7 3709.0 1095.7 50' 4463.1 4476.5 3720.9 1102.2 780 10' 4489.9 3732.7 1108.6 20' 4503.4 3744.6 1115.1 3756.5 1121.7200 C. 30' 4516.9 40' 4530,4 3768.5 1128.2 T 3780.4 1134.8 1.02 50' 4544.0 E 770o 4557.6 3792.4 1141.4 3804.4 1148.0 .321 10' 4571.2 20' 4584.8 3816.4 1154.7 4598.5 30' 3828.4 1161.3 40' 4612.2 3840.5 1168.1 50' 4626.0 3852.6 1174.8 4639.8 780 3864.7 1181.6 3876.8 1188.4 250 C. 10' 4653.6 T 20' 4667,4 3889.0 1195.2 3901.2 1202.0 1.28 30' 4681.3 E 40' 4695.2 3913.4 1208.9 50' 4709.2 3925.6 1215.8 .403 4723.2 790 3937.9 1222.7 3950.2 1229.7 10' 4737.2 4751.2 20' 3962.5 1236.7 30' 4765.3 3974.8 1243.7 40' 4779.4 3987.2 1250.8 3999.5 1257.9 300 C. 50' 4793.6 T 4807.7 800 4011.9 1265.0 10' 4822.0 4024.4' 1272.1 1.54 E 20' 4036.8 1279.3 30' 4850.5 4049.3 1286.5 .485 40' 4864.8 4061.8 1293.6 4074.4 1300.9 "' 50' 4879.2

---- ""'

E

Rtin'1/91

1=80o

E

1308.2 1315.6 + 1322.9 1330.3 5* C. T 1337.7 .30 1345.1 1352.6 1360.1 1367.6 1375.2 1382.8 1390.4

E .110

1398.0 100 C. 1405.7 1413.5 .61 1421.2 E 1429.0 .220 1436.8 1444.6 1452.5 1460.4 1468.4 1476.4 1484.4 150 C 1492.4 1500.5 1508.6 1516.7 1524.9 1533.1

.E

.332

1541.4 1549.7 1558.0 1566.3 20o C, 1574.7 1583.1 1.22

E 1591.6 1600.1 .445 1608.6 1617.1 1625.7 1634.4 1643.0 1651.7 250 C. 1660.5 T 1.53 1669.2 1678.1 E 1686.9 .558 1695.8 1704.7 1713.7 1722.7 1731.7 1740.8 300 C. T 1749.9 1759.0 E 1768.2 .671 1777.4 1786.7 1796.0

I

$10

E

T

4893.6 4908.0 4922.5 4937.0 40". 4951.5 50' 4966.1 820 4980.7 10' 4995.4 20' 5010.0 30' 5024.8 40' 5039.5 50' 5054.3 5069.2 830 10' 5084.0 20' 5099.0 30' 5113.9 40' 5128.9 50' 5143.9 840 5159.0 10' 5174.1 20' 5189.3 30' 5204.4 40' 5219.7 50' 5234.9 850 5250.3 10' 5265.6 20' 5281.0 30' 5296.4 40' 5311.9 50' 5327.4 86o 5343.0 10' 5359.6 20' 5374.2 30' 5389.9 40' 5405.6 50' 5421.4 5437.2 870 10' 5453.1 20' 5469.0 30. 5484.9 40' 5500.9 50' 5517.0 880 5533.1 10' 5549.2 20' 5565.4 30' 5581.6 40' 5597.8 50' 5614.2 5630.5 890 10' 5646.9 20' 5663.4 30' 5679.9 40' 5696.4 50' 5713.0 5729.7 o90 10' 5746.3 20' 5763.1 30' 5779.9 40' 5796.7 50' 5813.6 10' 20' 30'

E = R exsec IA 1

1=900

1805.3 1814.7 + 1824.1 1833.6 5 TC. 1843.1 .36 1852.6 E 1862.2 .149 1871.8 1881.5 1891.2 1900.9 1910.7 (1920.5 100 C. 1930.4 T 1940.3 .72 1950.3 E 1960.2 .299 1970.3 1980.4 1990.5 2000.6 2010.8 2021.1 2031.4 150 C. T 2041.7 2052.1 .E 2062.5 *450 2073.0 2083.5 2094.1 2104.7 2115.3 2126.0 2136.7 20o. C. T 2147.5 2158.4 1.45 E 2169.2 2180.2 .603 2191.1 2202.2 2213.2 2224.3 2235.5 2246.7 250 C. T 2258.0 2269.3 1.83 2280.6 E 2292.0 .756 2303.5 2315.0 2326.6 2338.2 2349.8 2361.5 300 C. T 2373.3 2385.1 2.20 E 2397.0 2408.9 .910 2420.9 2432.9

'''~

'

"

TABLE VIII TANGENTS AND EXTERNALS TO A 10 CURVE I

T

910 5830.5 10' 5847.5 20' 5864.6 30' 5881.7 40' 5898.8 50' 5916.0 92o 5933.2 10' 5950.5 20' 5967.9 30' 5985:3 40' 6002.7 50' 6020.2 93o 6037.8 10' 6055.4 20' 6073.1 30' 6090.8 40' 6108.6 50' 6126.4 940 6144.3 10' 6162.2 20' 6180.2 30' 6198.3 40' 6216.4 50' 6234.6 9o0 6252.8 10' 6271.1 20' 6289.4 30' 6307.9 40' 6326.3 6344.8 *50' 6363.4 10' 6382.1 20' 6400.8 30' 6419.5 40' 6438.4 50' 6457.3 70 6476.2 10' 6495.2 20' 6514.3 30' 6533.4 40' 6552.6 50' 6571.9 98o 6591.2 10' 6610.6 20' 6630.1 30' 6649.6 40' 6669.2 50' 6688.8 990 6708.6 10" 6728.4 20' 6748.2 30' 6768.1 40' 6788.1 50' 6808.2 1000 6828.3 10' 6848.5 6868.8 30' 6889.2 40' 6909.6 50' 6930.1

E 2444.9 2457.1 2469.3 2481.5 2493.8 2506.1 2518.5 2531.0 2543.5 2556.0 2568.6 2581.3 2594.0 2606.8 2619.7 2632.6 2645.5 2658.5 2671.6 2684.7 2697.9 2711.2 2724.5 2737.9 2751.3 2764.8 2778.3 2792.0 2805.6 2819.4 2833.2 2847.0 2861.0 2875.0 2889.0 2903.1 2917.3 2931.6 2945.9 2960.3 2974.7 2989.2 3003.8 3018.4 3033.1 3047.9 3062.8.

3077.7 3092.7 3107.7 3122.9 3138.1 3153.3 3168.7 3184.1 3199.6 3215.1 3230.8 3246.5 3262.3

I=1

1

1010 6950.6 "10' 6971.3 0 20' 6992.0 5 C. T 30' 7012.7 40' 7033.6 .43 E 50' 7054.5 .200 1020 7075.5 10' 7096.6 20' 7117.8 30' 7139.0 40' 7160.3 50' 7181.7 10 C. 103O 7203.2 10' 7224.7 T 20' 7246.3 .86 7268.0 30' E 40' 7289.8 .401 50' 7311.7 1040o 7333.6 10' 7355.6 20' 7377.8 30' 7399.9 40' 7422.2 150 C. 50' 7444.6 1.30 1050 7467.0 10'lop7489.6 E 20' 7512.2 .604 30' 7534.9 40' 7557.7 50' 7580.5 1060o 7603.5 10' 7626.6 20' 7649.7 200 C 30' 7672.9 T 40' 7696.3 1.74 50' 7719.7 E 7743.2 .809 1070 10' 7766.8 20' 7790.5 30' 7814.3 40' 7838.1 50' 7862.1 1080 7886.2 10' 7910.4 25eC 20' 7934.6 T 30' 7959.0 2.18 40' 7983.5 E 50' 8008.0 1.02 1090 8032.7 10' 8057.4 20' 8082.3 30' 8107.3 40' 8132.3 50' 8157.5 30 C 1100 8182.8 T 10' 8208.2 2.62 20' 8233.7 1.22 30' 8259.3 40' 8285.0 50' 8310.8

1.22

T=RtaWAl

L=1tooi

E

3278.1 3294.1 3310.1 3326.1 3342.3 3358.5 3374.9 3391.2 3407.7 3424.3 3440.9 3457.6 3474.4 3491.3 3508.2 3525.2 3542.4 3559.6 3576.8 3594.2 3611.7 3629.2 3646.8 3664.5 3682.3 3700.2 3718.2 3736.2 3754.4 3772.6 3791.0 3809.4 3827.9 3846.5 3865.2 3884.0 3902.9 3921.9 3940.9 3960.1 3979.4 3998.7] 4018.2 4037.8 4057.4 4077.2 4097.1 4117.0 4137.1 4157.3 4177.5 4197.9 4218.4 4239.0 4259.7 4280.5 4301.4 4322.4 4343.6 4364.8

I

I

111 10' + 20' So C. 30' T .51 40' E 50' .268 1120 10' 20' 30' 40' 50' 100 C. 1130 10' 20' .103 30' E 40' .536 50' 114 10' 20' 30' 40' 150 C. 50' 1.56 115 10' E 20' .806 30' 40' 50' 1160 10' 20'0 200 C. 30' 40' T 50' 2.08 E 1172 1.08 10' 20' 30' 40' 50' 1180 10' 250C 20' T 30' 2.61 40' E 50' 1.36 1190 10' 20' 30' 40' 50' 300C. 1200 10' 3.14 E g4,g 20' 30' 40' 50'

E= R exsec'it I

T

8336.7 8362.7 8388.9 8415.1 8441.5 8468.0 8494.6 8521.3 8548.1 8575.0 8602.1 8629.3 8656.6 8684.0 8711.5 8739.2 8767.0 8794.9 8822.9 8851.0 8879.3 8907.7 8936.3 8965.0 8993.8 9022.7 9051.7 9080.9 9110.3 9139.8 9169.4 9199.1 9229.0 9259.0 9289.2 9319.5 9349.9 9380.5 9411.3 9442.2 9473.2 9504.4 9535.7 9567.2 9598.9 9630.7 9662.6 9694.7 9727.0 9759.4 9792.0 9824.8 9857.7 9890.8 9924.0 9957.5 9991.0, 10025.0 10059.0 10093.0

e

4386.1 4407.6 4429.2 4450.9 4472.7 4494.6 4516.6 4538.8 4561.1 4583.4 4606.0 4628.6 4651.3 4674.2 4697.2 4720.3 4743.6 4766.9 4790.4 4814.1 4837.8 4861.7 4885.7 4909 9 4934.1 4958.6 4983 1 5007.8 5032.6 5057.6 5082.7 5107.9 5133.3 5158.8 5184.5 5210.3 5236.2 5262.3 5288.6 5315.0 5341.5 5368.2 5395.1 5422.1 5449.2 5476.5 5504.0 5531.7 5559.4 5587.4 5615.5 5643.8 5672.3 5700.9 5729.7 5758.6 5787.7 5817.0 5846.5 5876.1

1-1206

+ T .62 E .360

10* C. T 1.25 SE

721

150 C. 1.93 E 109

20 C. T 2.52 E 1.46

250C. T 3.16 E 1.83

300C.

T 3.81 E 2.20

TABLE IX MIDDLE ORDINATES OF RAILS Length of Rail (feet)

C

R

o

Feet

0-20 0-40 1-0 1-20 1-40 2 -0 2-20 2-40 3-0 3-20 3-40 4-0 4-20 4-40 5 6 7

17189 8594 5730 4297 3438 2865 2456 2149 1910 1719 1563 1433 1323 1228 1146 955.3 819.0

30

28

26

-24

22 20 C

Inch Inch lfch Inch Inch lach 0 .08 .07 .06 .05 .16 .14 .12 .10 .24 .20 .18 .15 .31 .27 .23 .20 .39 .34 .29 .25 .47 .41 .35 .30 .55 .48 .41 .35 .63 .55 .47 .40 .62 .53 .45 .71 .78 .68 .59 .50 .86 .75 .65 .55 .94 .82 .71 .60 1.02 .89 .77 .65 1.10 .96 .83 .70 1.18 1.03 .89 75 1.41 1.23 1.06 .90 1.65 1.44 1.24 1.05

.04 .08 .13 .17 .21 .25 .29 .33 .38 .42 .46 .50 .55 .59 .63 .76 .89

.03 .07 .10 .13 .1.7 .20 .23 .27 .31 .35 .38 .42 .45 .48 .52 .62 .73

8 9 10 11 12 13 14 15 16 17 18 19 20 22 24 26

30

2 I2221 20

feet

lch

Inch Inch Inch

28

26

716.8 637.3 573.7 521.7 478.3 441.7 410.3 383.1 359.3 338.3 319.6 302.9 287.9 262.0 240.5 222.3

1.88 2.12 2.36 2.59 3.83 3.05 3.30 3.54 3.76 4.00 4.21 4.45 4.70 5.16 5.64 6.07

1.64 1.84 2.05 2.26 2.47 2.66 2.87 3.08 3.28 3.48 3.67 3.89 4.09 4.44 4.92 5.29

1.42 1.60 1.78 1.95 2.15 2.30 2.48 2.68 2.83 3.02 3.18 3.36 3.55 3.84 4.20 4.58

R

1.20 1.35 1.50 1.65 1.81 1.96 2.10 2.26 2.40 2.57 2.70 2.86 3.00 3.30 3.59 3.88

Inch

1.01 .84 1.14 .94 1.27 1.04 1.39 1.15 1.54 1.26 1.66 1.36 1.78 1.46 1.91 1.57 2.04 1.67 2.16 1.78 2.28 1.87 2.41 1.98 2.54 2.09 2;80 2.29 3.04 2.50 3.29 2.70

TABLE X SHORT RADIUS CURVES Radius

Chord

Central

Deflection

Angle

fIor 1 Foot

35 45 50 60 75 100 120 150 190 200 225 240 250 275 288 300 350 376 400 410

10 10 15 15 15 20 20 20 25 25 25 25 25 25 50 50 50 50 50 50

16-26 12-46 17-16 14-22 11-30 11-30 9-34 7-39 7-32 7--10 6-25 5 58 5 44 5 -12 9-58 9 -32 8-12 '-40 7-10 7--00

8-13 6-23 8-38 7--11 5-45 5-45 4-47 3-49 3--46 3-35 3-12 2-59 2-52 2-36 4 -59 4-46 .4-06 3-50 3-35 3- 30

49.3 38.3 34.5 28.8 23.0 17.3 14.3 11.5 9.15 8.6 7.7 7.2 6.9 6.2 6.0 5.7 4.9 4.6 4.3 4.2

Feet

Feet

Angle

Deflection

To find length of curve divide angle from P. C. to P. T. by central angle of chord, and multiply by length of chord.

TABLE

XI

INCLINED DISTANCE OF 100 FT. REDUCED TO HORIZONrAL Slope Slope 0000' 15' 30' 45' 1 00 15 30 45 2 00 15 30 45 3 00 15 30 45 4 00 15 30 45 5 00 15 30 45 600 15 30 45 7 00 15 30 45

orizontal Correction Distance 100.000 99.999 99.996 99.991 99.985 99.976 99.966 99.953 99.939 99.923 99.905 99.885 99.863 99.839 99.813 99.786 99.756 99.725 99.692 99.657 99.619 99.580 99.540 99.497 99.452 99.406 '99.357 99.307 99.255 99.200 99.144 99.087

Rise 0.000 0.004 0.009 0.013 0.017 0.022 0.026 0.031 0.035 0.039 0.044 0.048 0.052 0.057 0.061 0.065 0.070 0.074 0.078 0.083 0.087 0.092 0.096 0.100 0.105 0.109 0.113 0.118 0.122 0.126 0 .131 0.135

0.000 0.001 0.004 0.009 0.015 0,024 0.034 0.047 0.061 0.077 0.095 0.115 0.137 0.161 0.187 0.214 0.244 0.275 0.308 0.343 0.381 0.420 0.460 0.503 0.548 0.594 0.643 0.693 0.745 0.800 0.856 0.913

Slope 0

8 0Q' 15' 30' 45' 9 00 15 30 45 10 00, 15 30 45 11 00 15 30 45 12 00 15 30 45 13 00 15 30 45 14 00 15 30 45 15 O0 15 30 45

Horizontal Distance

Correction

Rise

99.027 98.965 98.902 98.836 98.769 98.700 98.629 98.556 98.481 98.404 98.325 98.245 98.163 98.079 97.992 97.905 97.815 97.723 97.630 97.534 97.437 97.338 97.237 97.134 97.030 96.923 96.815 96.705 96.593 96.479 96.363 96.246

0.973 1.035 1.098 1.164 1.231 1.300 1.371 1.444 1.519 1.596 1.675 1.755 1.837 1.921 2.008 2.095 2.185 2.277 2.370 2.466 2.563 2.662 2.763 2.866 2.970 3.077 3.185 3.295 3.407 3.521 3.637 3.754

0.139 0.143 0.148 0.152 0.156 0.161 0.165 0.169 0.174 0.178 0.182 0.18L 0.191 0.195 0.199 0.204 0.2068 0.212 0.216 0.221 0.225 0.229 0.233 0.238 0.242 0.246 0.250 0.255 0.259 0.263 0.267 0.271

For each foot take one one-hundredth of each reading.

TABLE XII

MINUTES IN DECIMALS OF A DEGREE.

0130"

1 00 30 2 00 30 3 00 30 4 00 30 5 00 30 6 00 30 700 30 8 00 30 900 30

10 00

.00833 10'30" .01667 11 00 .02500 30 .03333 12 00 30 .04167 .05000 13 00 .05833: 30 .06667 1114 00 .0750011 30 .08333 1500 .09167 30 .10000 1600 .10833 30 .1167 17 00 .12500 30 .13333 18 00 .14167 30 .15000 1900

.17500 .18333 .19167 .20000 .20833 .21667 .22500 .23333 .24167 .25000 .25833 .26667 .27500 .28333 .29167 .30000 .30833 .31667

.15833

.32500

30

.1667 2000

20'30" 21 00 30 22 00 30 2300 30 2400 30 2500 30 26 00 30 2700 30 28 00 30 2900 30

.33333 3000

.34167 30'30" .35000 31 00 .35833 30 .36667 32 00 .37500 30 .38333133 00 .39167 30 .40000 3400 .40833 30 .41667 3500 .42500 30 .43333 3600 .44167 30 .45000 3700 .45833 30 .46667 38 00 .47500 30 .48333 39 00

.50833 40'30" .51667 41 00 .52500 30 .53333114200 .54167 30 .55000 43 00 30 .55833 .566671144 00 .57500 30 .58333 4500 .59167 30 .0000 46 00 .60833 30 .61667 4700 .62500 30 .633334800 .64167 30 .650004900

.67500 50'30" ,68333 51 00 .69167 30 .70000 52 00 .70833 30 .71667 53 00 30 .72500 .73333 5400 .74167 30 .75000 55 00 .75833 30 .76667 5600 .77500 30 .78333 $7 00 .79167 30 .80000 5800 .80833 30 .816759 00

.49167

.65833

.82500

30

.50000 4000

30

.666675000

30

.83333 6000

.84167 .85000 .85833 .86667 .87500 .88333 .89167 .90000 .90833 .91667 .92500 .9333 .94167 .95000 .95833 .96667 .97500 .98333 .99167

1.00000

TABLE XIII--CORRECTIONS

FOR TANGENTS AND EXTERNALS

These corrections are to° be added to the approximate values, found by dividing the tangent, or external,for a 1 curve (Table V III) by the degree of curve, in order to obtain the true tangents, or externals. Intermediate values may be obtained by interpolation.

FOR TANGENTS ADD DzoRES Or CURVE

Central Angle

°

°

Angle10

10l 15.°

90 ° 2

.06 10

09 14

13 19

06 .08

.13 16

19 24

.26 .33

13 15

70

1T6° 80 88 °

90 ° 96° 100 ° 110 120

19 .29 22 .34

10 11

40 456 °

20"

03 04

80 856°

50° 55° 60 656 °

15

.26 .40 .30 44

°

°

35

°

40

45

.32 40

.39 .45 49 .58

50

°

°

55

60

.28 .31 34 45 .51 .53

.51 67

.58 .75

.65 .72 .83 90

°

°

70'

65

38 58

42 .63

.46 .68

79 .84 .90 .99 1.06 1.14

39 49 .59 .69 79 .89 .99 1.09 1.20 1.291.39 47 .58 .69 ,70 .81 .92 1.04 1.29 1.42 1.54 1.66 .80 .93 1.06 1.20 1.34 1.49 1.64 1.79 1.94

.34 38 42 46

25 .27 30 33

.51 761.02 .56 .83 1.12 .61 .91 1.22 '6 1.00 1.33

91 1.06 1.21 1.37 1.52 1.70 1.87 2.04 2.21

.51 .68 .85 1.02 .57 76 .95 1.14 .63 .84 1.05 1.27 .69 .93 1.16 1 40

36 .72 1.09 39 79 1.19 .43 .86 1.30 51 1.031.56

°

30

16 19 .22 .25 24 .29 .34 .39

.53 .67 60 76

17 19 .21 23

°

25°

1.45 1.55 1.74 2.08

1.19 1.32 1.49 1.64

1.36 1.54 1.72 1.52 1.72 1.92 1.71 1.94 2.17 1.88 2.13 2.38

1.91 2.14 2.38 2.63

2.10 2.35 2.60 2.88

2.06 2.27 2.46 2 70

2.88 3.16 3.44 3.77

3.163.443.72 3.47 3.78 4.09 3.78 4.12 4.46 4.14 4.55 4 8(

2.33 2.57 2 78 3.05

2.29 2.56 2.83 3.13

2.48 2.77 3.07 3.39

1.28 1.40 1.53 1.68

1.54 1.80 1.69 1.98 1.84 2.15 2.022.36

1.83 2.00 2.18 2..61

2.202.57 2.94 3.323.70 4.10 4.50 4.91 5.32 2.40 2.803.203.61 4.02 4.404.985.385.83 2.62 3.06 3.50 3.95 4.40 4.88 5.37 5.85 6.34 3.14 3.67 4.214 765.315 86 6.43 7 017 60

2.60 2.87 3.10 3.40

62 1.25 1 93 2.52 3.16 3.81 445 5.11 5.77 6 44 7 12 7.80 8.50 9 22

FOR EXTERNALS ADD DEGREE or CURVE

Central

Angle

°

5 °

10 165

0

°

10' 15

.001 .003 .003.007

20'

25'

30'

°

35

.004 .006 .007 .008 .009 .010 .014 .018 .023 .027

45

40'

°

.011 .012 .029 .032

500

55

°

.014 .015 .035 .. 03

°

600

65

.017 .043

.018 .020 .047 .051

70'

.006 .011 .017 .022 .028 .034 .038 .045 .051 .057

.063 .070 .076 .088

.009 .018 .027

086 .046

.056 .065

.074

.083 .093

.106

127

135

.013.025 .018.035 .023 .046 .030 .060

.038 .054 .070 .093

.051 .072 .093 .11

.065 .086 .117 .153

.078 .109 .141 .141 .184

.090 .131 .117 .172 .172 .216

.103 .153 .203 .203 .254

.116 .175 .234 .289

.129 .197 .265 .325

.149 .170 .213 .230 .27777 90 .351 .378

.179 .247 .315 .411

.188 .264 .341 .445

6S

.037.075 .046.093 .056.112 .067.135

.116 .142 .168 .204

.151 .188 .225 .273

.189 .236 .283 .343

.227 .283 .340 .412

.266 .332 .398 .483

.305 .381 .457 .554

.345 .420 .516 .625

.34 .479 .575 .697

.425 .530 .636 .711

.508 .641 .774 .922

70° 7' s0 856

.080 .159 .095 .182 .110.220 .128.259

.240 .321 .403 .286 .383 .480 .332 .445 .558 .391 .524 .657

.485 .578 .671 .790

.568 .678 .787 .926

.149.299 .174.350 .200.401 .268.536

.450 .522 .604 .806

.603 .756 .706 .985 .809 1.01 1.08 1.35

.910 1.06 1.22 1.63

1.45 1.82

2.19 2.57

251

W°

85 40° 45

60

°

685

o60

°

90 ° 96 ° 100 110 110

°

.360 .721 1.08

120

.467 .582 .697 .845

.652 .735 .819 .906 .994 .777 .877 .977 1.07 1.18 .903 1.02 1.13 1.25 1.38 1.06 1.20 1.34 1.47 1.62

1.08 1.29 1.50 1.76

1.17 1.39 1.62 1.91

1.54 1.80 2.06 2.76

1.70 1.99 2.28 3.05

1.87 2.18 2.50 3.35

2.03 2.38 2.73 3.66

2.20 2.58 2.96 3.96

3.33 3.72

4.11

4.50 4.91

5.32

1.07 1.22 1.38 1.25 1.43 1.62 1.43 1.64 1.85 1.91 2.20 2.48 2.95

.550 .700 .851 1.01

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A foremost authority on fish flies, predicts Dubuque's biggest on' slaught of. the season is just

J

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telegraph Herald, Dubuque, Iowa, Sunday, July 2, 1978

around the corner. ....... Page 12.

, return.next week swarms likel .to

Fs si

Fish

.. . .% . . . y

B3y KATHY SCHWAR S Telegraph Herald Staff Writer

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All' Calvin Fremling needed to hbar Friday was the phrase "fish flies," and he responded: "Don't tell me, I would guess, the night before last you had a big emergence of fish flies."

Amazing. He wasn't even in Dubuque, Wednesday.

But the Winona State University biology professor knew he was right, even from up there in Winona, Minn. He's been watching those insects for 22 years now, and he probably knows more about when they'll rise from the river than they do.

Wednesday's swarm in Dubuque was paralleled by similar emergences in LaCrosse and Alma, Wis., and "all over," he said. Here it bugged city recreation baseball, teams so badly that Kunnert's and Pusateri's teams cancelled their game by the third inning around 9:30 p.m. In previous years, accidents have been attributed to vehicles slipping on the 'thick layers of fish , flies covering streets and windshields, Ed Cawley, biology professor at Dubuque's Loras

College, says, "'They don't do much bad, other than being a nuisance. They just swarm all over the city and make it smell fishy for a while." The inch-long, creatures don't even bite, ,he says. They usually don't have mouths,.

The fish fly, or May fly, emergence is an annual occurrence near rivers worldwide, but Dubuque lies in a prime fish fly area for several reasons including less polluted breeding water, Fremling says. But the small emergences more than a week ago, and what appeared to be a large emergence this week probably weren't the "big splash" "I wbuld guess you're due for a bigger one between, the 9th and the 12th," Fremling said. "I'd be 90 per cent confident that's when it'll occur." He added a lot depends on the wind. Without the wind blowing the fragile wisps into town, most residents wouldn't see them., Fish flies are an "excellent indicator 'of general water quality," Fremllng says. The immature nymphs live for about a year in mud at the bottom of the river, usually the pool below the dam, and feed on orra-~~

ganic debris. If silt builds up greatly, they get buried, and if pollution decreases oxygen in the river, they may suffocate. They emerge to mate for 24 to 48 hours, lay eggs in the river up to 10 miles upstream. atd die.

And that's all they're supposed to do.

But city lights attract them. and winds contro' their fate, so many often wind up as far west of the riv er The Dubuque area hosts Cw. main species of the Ephemeral ("here today, gore tomorrow") Heoxgenia insects. The light yellow limbata usually emerge first.

The more common, dark ones are bilirneata. or as Fremling ays'ship Captains tag them, "big, black bastards."

The professionals don't'belittle the nuisance, calling the flies an important part of the river ecosystem.

Fremling says for a close-up look at the May fly (most species emetrge in May), Encyclopaedia P1itin nica has produced, with Fremlitig as consultant, a 20minute color film that examines the fly from one end ,of the screen to the other. He says it's loaned out worldwide.

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AMOCO AMOCO i Super

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Washington: The monthly service charge may not lawfully exceed the greaterof on percent of the outstanding balance(twelve percent per year computed monthly) or on d lar.

VBuyer's gnat uhre 090-D (3-77)

" Approval Code â&#x20AC;˘

Lic.No.& State

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* Donot sign this Buyer:

agreement (see back side) before you read it or if it contains any blank spaces. * You are entitled to a completely filled-in AAIDgg copy of this agreement at the time you sign it- Keep it to protect your legal rights * You may at any time pay off the full unpaidbalanceunder this agreement.

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S Totals must agree

"" "~' CUST6MER'S COPY

Federal.

State andLocalTaxes,whten applicable areincluded inpriceand amount,unless separately stated.

AMOCO ....

105851 LEAD - FREE LEADER

Revolving ChargeAccount Agreement RetailInstallment Credit Agreement(New York) Consumer Credit Document(North Carolina) The terms of Amoco Oil Company's revolving charge account agreement disclosed at time of issuance of credit card, as modified by subsequent changes to date, if any, are incorporated herein and made part hereof by reference.

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